Question: Simplify the following expression: $q = \dfrac{p^2 - 3p - 54}{p - 9} $
Solution: First factor the polynomial in the numerator. $ p^2 - 3p - 54 = (p - 9)(p + 6) $ So we can rewrite the expression as: $q = \dfrac{(p - 9)(p + 6)}{p - 9} $ We can divide the numerator and denominator by $(p - 9)$ on condition that $p \neq 9$ Therefore $q = p + 6; p \neq 9$